[Algèbres de Hecke affine double, co-invariants conformes et polynômes de Kostka]
Nous étudions la classe de représentations, qui s'appelle les représentations calibrées, de l'algèbre de Hecke affine double rationnelle/trigonométrique de type . Nous réalisons les modules simples calibrés comme des espaces de co-invariants construits de modules intégrables sur l'algèbre de Lie affine . En plus, nous donnons une formule de caractère de ces modules simples en terme d'une généralisation des polynômes de Kostka. Ces résultats sont conjecturés par Arakawa, Suzuki et Tsuchiya en se basant sur la théorie de champs conformes. Pour leur démonstration, nous utilisons les résultats récents de la théorie des représentations de l'algèbre de Hecke affine double. Les détails seront donnés dans des publications ultérieures.
We study a class of representations called ‘calibrated representations’ of the rational and trigonometric double affine Hecke algebras of type . We give a realization of calibrated irreducible modules as spaces of coinvariants constructed from integrable modules over the affine Lie algebra . We also give a character formula of these irreducible modules in terms of a generalization of Kostka polynomials. These results are conjectured by Arakawa, Suzuki and Tsuchiya based on the conformal field theory. The proofs using recent results on the representation theory of the double affine Hecke algebras will be presented in the forthcoming papers.
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@article{CRMATH_2006__343_6_383_0,
author = {Suzuki, Takeshi},
title = {Double affine {Hecke} algebras, conformal coinvariants and {Kostka} polynomials},
journal = {Comptes Rendus. Math\'ematique},
pages = {383--386},
publisher = {Elsevier},
volume = {343},
number = {6},
year = {2006},
doi = {10.1016/j.crma.2006.08.009},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2006.08.009/}
}
TY - JOUR AU - Suzuki, Takeshi TI - Double affine Hecke algebras, conformal coinvariants and Kostka polynomials JO - Comptes Rendus. Mathématique PY - 2006 SP - 383 EP - 386 VL - 343 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.08.009/ DO - 10.1016/j.crma.2006.08.009 LA - en ID - CRMATH_2006__343_6_383_0 ER -
%0 Journal Article %A Suzuki, Takeshi %T Double affine Hecke algebras, conformal coinvariants and Kostka polynomials %J Comptes Rendus. Mathématique %D 2006 %P 383-386 %V 343 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2006.08.009/ %R 10.1016/j.crma.2006.08.009 %G en %F CRMATH_2006__343_6_383_0
Suzuki, Takeshi. Double affine Hecke algebras, conformal coinvariants and Kostka polynomials. Comptes Rendus. Mathématique, Tome 343 (2006) no. 6, pp. 383-386. doi : 10.1016/j.crma.2006.08.009. http://www.numdam.org/articles/10.1016/j.crma.2006.08.009/
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